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A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.

%I A210495 #26 Apr 15 2025 09:41:02
%S A210495 1,2,3,4,5,10,11,12,15,18,22,23,24,27,29,30,32,34,39,41,42,45,52,53,
%T A210495 54,56,57,58,63,64,68,69,76,83,84,87,89,93,96,108,110,113,115,131,142,
%U A210495 144,147,150,152,153,156,162,165,168,170,172,173,175,177
%N A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.
%C A210495 This is the union of Sophie Germain primes and Sophie Germain nonprimes, so it might be called "Sophie Germain numbers".
%H A210495 Harvey P. Dale, <a href="/A210495/b210495.txt">Table of n, a(n) for n = 1..1000</a>
%H A210495 J. S. Gerasimov, <a href="https://web.archive.org/web/20201230073136/http://list.seqfan.eu/pipermail/seqfan/2013-January/010687.html">Sophie Germain nonprimes</a> [title corrected], SeqFan mailing list, Jan 15 2013.
%p A210495 A210495 := proc(n)
%p A210495     option remember;
%p A210495     local a;
%p A210495     if n = 1 then
%p A210495         1 ;
%p A210495     else
%p A210495         for a from procname(n-1)+1 do
%p A210495             if isprime(numtheory[tau](a)*a+1) then
%p A210495                 return a;
%p A210495             end if;
%p A210495         end do:
%p A210495     end if;
%p A210495 end proc: # _R. J. Mathar_, Jan 27 2013
%t A210495 Select[Range[200],PrimeQ[# DivisorSigma[0,#]+1]&] (* _Harvey P. Dale_, Aug 26 2013 *)
%o A210495 (PARI) is(n)=isprime(numdiv(n)*n+1) \\ _Charles R Greathouse IV_, Jan 24 2013
%Y A210495 Cf. A083271, A005384, A209271, A000005.
%K A210495 nonn
%O A210495 1,2
%A A210495 _Juri-Stepan Gerasimov_, Jan 24 2013